US20130004364A1 - Al-based bearing alloy - Google Patents

Al-based bearing alloy Download PDF

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Publication number
US20130004364A1
US20130004364A1 US13/583,823 US201113583823A US2013004364A1 US 20130004364 A1 US20130004364 A1 US 20130004364A1 US 201113583823 A US201113583823 A US 201113583823A US 2013004364 A1 US2013004364 A1 US 2013004364A1
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US
United States
Prior art keywords
particle
bearing alloy
particles
mass
based bearing
Prior art date
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Abandoned
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US13/583,823
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English (en)
Inventor
Moritaka Fukuda
Tomoyuki NIRASAWA
Yukihiko Kagohara
Shigero Inami
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Daido Metal Co Ltd
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Daido Metal Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Daido Metal Co Ltd filed Critical Daido Metal Co Ltd
Assigned to DAIDO METAL COMPANY LTD. reassignment DAIDO METAL COMPANY LTD. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: FUKUDA, MORITAKA, INAMI, SHIGERU, KAGOHARA, YUKIHIKO, NIRASAWA, TOMOYUKI
Publication of US20130004364A1 publication Critical patent/US20130004364A1/en
Assigned to DAIDO METAL COMPANY LTD. reassignment DAIDO METAL COMPANY LTD. ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: FUKUDA, MORITAKA, INAMI, SHIGERU, KAGOHARA, YUKIHIKO, NIRASAWA, TOMOYUKI
Abandoned legal-status Critical Current

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    • C—CHEMISTRY; METALLURGY
    • C22—METALLURGY; FERROUS OR NON-FERROUS ALLOYS; TREATMENT OF ALLOYS OR NON-FERROUS METALS
    • C22C—ALLOYS
    • C22C21/00—Alloys based on aluminium
    • C22C21/02—Alloys based on aluminium with silicon as the next major constituent
    • C—CHEMISTRY; METALLURGY
    • C22—METALLURGY; FERROUS OR NON-FERROUS ALLOYS; TREATMENT OF ALLOYS OR NON-FERROUS METALS
    • C22C—ALLOYS
    • C22C21/00—Alloys based on aluminium
    • C—CHEMISTRY; METALLURGY
    • C22—METALLURGY; FERROUS OR NON-FERROUS ALLOYS; TREATMENT OF ALLOYS OR NON-FERROUS METALS
    • C22C—ALLOYS
    • C22C21/00—Alloys based on aluminium
    • C22C21/06—Alloys based on aluminium with magnesium as the next major constituent
    • C22C21/08—Alloys based on aluminium with magnesium as the next major constituent with silicon
    • C—CHEMISTRY; METALLURGY
    • C22—METALLURGY; FERROUS OR NON-FERROUS ALLOYS; TREATMENT OF ALLOYS OR NON-FERROUS METALS
    • C22C—ALLOYS
    • C22C21/00—Alloys based on aluminium
    • C22C21/10—Alloys based on aluminium with zinc as the next major constituent
    • C—CHEMISTRY; METALLURGY
    • C22—METALLURGY; FERROUS OR NON-FERROUS ALLOYS; TREATMENT OF ALLOYS OR NON-FERROUS METALS
    • C22C—ALLOYS
    • C22C21/00—Alloys based on aluminium
    • C22C21/12—Alloys based on aluminium with copper as the next major constituent
    • C22C21/14—Alloys based on aluminium with copper as the next major constituent with silicon
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C33/00—Parts of bearings; Special methods for making bearings or parts thereof
    • F16C33/02—Parts of sliding-contact bearings
    • F16C33/04—Brasses; Bushes; Linings
    • F16C33/06—Sliding surface mainly made of metal
    • F16C33/12—Structural composition; Use of special materials or surface treatments, e.g. for rust-proofing
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C33/00—Parts of bearings; Special methods for making bearings or parts thereof
    • F16C33/02—Parts of sliding-contact bearings
    • F16C33/04—Brasses; Bushes; Linings
    • F16C33/06—Sliding surface mainly made of metal
    • F16C33/12—Structural composition; Use of special materials or surface treatments, e.g. for rust-proofing
    • F16C33/121—Use of special materials
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
    • F16C—SHAFTS; FLEXIBLE SHAFTS; ELEMENTS OR CRANKSHAFT MECHANISMS; ROTARY BODIES OTHER THAN GEARING ELEMENTS; BEARINGS
    • F16C2204/00—Metallic materials; Alloys
    • F16C2204/20—Alloys based on aluminium

Definitions

  • the present invention relates to an Al-based bearing alloy containing Si.
  • An Al-based bearing alloy such as an Al—Sn bearing alloy containing approximately 20 mass % of Sn, and Al—Sn—Si bearing alloy containing approximately 10 mass % of Sn, and 3 mass % of Si are being used in slide bearings for automobiles and industrial machines in general.
  • the Al-based bearing alloy when being used as a slide bearing, is normally bonded with a metal backing made of a steel sheet.
  • Si contained in the Al-based bearing alloy is a hard particle and thus, smoothens the protrusions of the countershaft when it contacts the countershaft (lapping effect). Further because the hard particle plays a sacrificial role in contacting the countershaft, the Al matrix becomes difficult to scrape off, thereby improving wear resistance.
  • Recent automobile engines are designed to go through the start-stop cycle on a frequent basis for better mileage. Further, housings such as connecting rods, into which slide bearings are installed, are becoming lighter in weight. Thinning, which is a typical approach for obtaining a lighter housing, reduces the strength of the housing and makes the housing deformation prone. Housing is thus, easily deformed by forces such as the dynamic load of the counter shaft. As a result, the Al-based bearing alloy (slide bearing), which supports the counter shaft, also becomes deformation prone and consequently fatigue prone.
  • patent document 1 teaches an Al-based bearing alloy containing Si such that small Si particles and large Si particles are mixed in an suitable ratio to achieve improvement in both wear resistance and fatigue resistance.
  • Patent Document 1 JP 2003-119530 A
  • the present invention is based on the above described background and one object of the present invention is to provide an Al-based bearing alloy with further improvements in wear resistance and fatigue resistance.
  • the Al-based bearing alloy according to claim 1 of the present invention include 1 to 15 mass % of Si, wherein an average of A/a is greater than 1 and equal to or less than 4, where A represents a distance between adjacent Si particles residing on a sliding-side surface, and a represents a length of a major axis of the Si particles.
  • the image of the Si-containing Al-based bearing alloy structure is captured on the sliding-side surface and the captured image is put through software analysis to obtain the required parameters.
  • FIG. 1 is an image produced by the analysis showing idealized distribution of Si particles 1 .
  • the lines drawn between the adjacent Si particles 1 are Voronoi boundaries. Length a of the major axis of Si particle 1 shown in FIG.1 is assumed as the longer side of a circumscribing quadrangle surrounding Si particle 1 . Then, distance A between the gravitational centers of the adjacent Si particles 1 is divided by length a of the major axis of Si particle 1 . This is repeated for each Si particle 1 within a given area of observation to obtain the average A/a.
  • Si particles 1 are evenly distributed with suitable spacing within the Al matrix. When in such even distribution, Si particle 1 is expected to exert lapping effect and wear resistance as well as fatigue resistance which are properties of a hard particle inherently possessed by Si particle 1 .
  • the Al matrix occupies relatively greater percentage of the structure and thus, degrades the lapping effect and the wear resistance in particular.
  • the average of A/a is equal to or less than 1
  • the Al matrix occupies relatively less percentage of the structure and thus, the ductility required in a bearing alloy is degraded which causes a sudden and significant degradation in conformability and degradation in fatigue resistance.
  • the Al-based bearing alloy of the present invention is manufactured as follows.
  • a material of Al, Si, and required additives are formed into a billet sheet of Al-based bearing alloy by typically using a continuous caster. Then, the billet is rolled repeatedly to a predetermined thickness. The billet is rolled at least twice at a high rolling reduction. More specifically, the first roll is carried out at a rolling reduction ranging from 40 to 80%. The second roll is carried out at a rolling reduction ranging from 30 to 70%. The rolling reduction of the (n+1)th roll is preferably lower than the rolling reduction of the nth roll.
  • the destruction of the crystal grains is defined as a state in which the crystal grain boundaries of Al are excessively dense and hence cannot be distinguished from one another in the cross sectional sample of the structure obtained by etching.
  • the rolling when carried out to the extent to destroy the crystal grains, can be considered to have caused the Si particles to be evenly distributed within the Al matrix.
  • Al is re-crystallized through heat treatment. It is thus, assumed that the Si particles are distributed within the Al matrix as evenly as possible and that the Si particles are shaped in a suitable form.
  • an average aspect ratio of the Si particles residing on the sliding-side surface is equal to or greater than 1 and equal to or less than 2.5.
  • the aspect ratio of the Si particle is given by dividing the longer side (major axis) of the circumscribing quadrangle of Si particle 1 shown in FIG.1 by the shorter side (minor axis).
  • the Si particle approximates a circle or a square as the aspect ratio approximates 1 and the Si particle becomes more and more elongate as the aspect ratio becomes greater.
  • the shape of the Si particle is closely related to the fatigue resistance of the bearing alloy.
  • the aspect ratio of the Si particle indicates the degree of anisotropy in the shape of the Si particle.
  • the Si particle with a large aspect ratio has relatively larger degree of anisotropy in its shape and is subjected to force with priority.
  • Si particles with relatively larger degree of anisotropy render the bearing alloy to be deformation prone and therefore tend to degrade the fatigue resistance of the bearing alloy.
  • the average aspect ratio of the Si particles is preferably 1 or more and 2.5 or less.
  • the Al-based bearing alloy of the present invention may be manufactured by repeating the rolling of the billet for obtaining the predetermined thickness by carrying out the first roll at a rolling reduction of 50 to 70%, and the second roll at a rolling reduction of 40 to 60%.
  • the (n+1)th roll is preferably lower than the rolling reduction of the nth roll by 10%. For instance, if the rolling reduction of the nth roll is 60%, the rolling reduction of the (n+1)th roll is to be set to 50%.
  • a given specific Si particle residing on the sliding-side surface and a closest Si particle adjacent to the specific particle in the thickness direction are spaced from one another such that the closest Si particle resides within radius r being taken from a gravitational center of the specific Si particle and being given by:
  • A represents a distance from the specific particle to the adjacent Si particle on the sliding-side surface, and a represents a length of a major axis of the specific Si particle.
  • the direction indicated by D denotes the direction of thickness.
  • the distribution of Si particles 11 , 12 , 13 , and 14 on surface 10 of the sliding side and the distance to the closest adjacent Si particles 21 , 22 , and 23 in the thickness direction is closely related to wear resistance. More specifically, when distance from given specific Si particles 11 , 12 , 13 , and 14 to their closest adjacent Si particles in the thickness direction is equal to or greater than a predetermined distance, wear resistance is further improved. In contrast, if the distance from each of the given specific Si particles 11 , 12 , 13 , and 14 to their closest adjacent Si particles 21 , 22 , and 23 is too far, wear resistance tends to degrade.
  • the Si particles 21 , 22 , and 23 each being in the closest adjacency in the thickness direction to the given specific Si particles 11 , 12 , 13 , and 14 have been located within region 30 defined by predetermined radius r measured from each of the given specific Si particles 11 , 12 , 13 , and 14 .
  • r measured from each of the given specific Si particles 11 , 12 , 13 , and 14 .
  • Each of the closest adjacent Si particles 21 , 22 , and 23 need not be entirely within but may be partly within region 30 defined by radius r measured from the specific particles 11 , 12 , and 14 .
  • the distribution of the Si particles in the thickness direction can be controlled as follows.
  • the produced billet is rolled at least twice. More specifically, the first roll is carried out at the rolling reduction ranging from 40 to 80% and preferably from 50 to 70%.
  • the second roll is preferably carried out at the rolling reduction which amounts to 60 to 95% of the rolling reduction employed in the first roll.
  • the crystal grains of the Al matrix within the Al-based alloy is thus destroyed to control the location of the Si particles adjacent to one another in the thickness direction.
  • the (n+1)th roll is carried out at the rolling reduction which amounts to 60 to 95% of the rolling reduction employed in the nth roll.
  • the coefficient B was defined to be greater than a/2 and equal to or less than 20, however, for the convenience of measurement, the value of a which is required to specify the value of a/2 is set to the average value obtained from each of length a of the major axis within the predetermined area of observation.
  • the closest adjacent Si particle is preferably within the range surrounded by 2a/3 ⁇ r ⁇ 15 ⁇ (A/a) in view of improving wear resistance and fatigue resistance.
  • the value a for specifying the value of 2a/3 is set to the average value obtained from each of length a of the major axis within the predetermined area of observation.
  • radius r for defining region 30 is preferably equal to or greater than 2 ⁇ m and equal to or less than 50 ⁇ m in the manufacturing point of view.
  • the gravitational distance between a given specific Si particle and the closest adjacent Si particle being 5 ⁇ m or greater is advantageous in view of fatigue resistance and being 30 ⁇ m or less is advantageous in view of wear resistance.
  • the Al-based bearing alloy according to claim 4 of the present invention includes one or more of:
  • the components (1) to (3) are limited to the above described composition based on the following reasoning.
  • the selective elements (Cu, Zn, Mg) given in (1) are additive elements for improving the strength of the Al matrix and may be forcibly incorporated by solid solution into the Al matrix through solution heat treatment and may be allowed to precipitate fine compounds by aging. This effect cannot be expected in content less than 0.1 mass % and will produce bulky compounds in content greater than 7 mass %. Total content preferably ranges from 0.5 to 6 mass %.
  • the selective elements (Mn, V, Mo, Cr, Co, Fe, Ni, W) given in (2) are additive elements for improving fatigue resistance and may be incorporated alone by solid solution into the Al matrix or may be crystallized as a multi-element intermetallic compound. This effect cannot be expected in content less than 0.01 mass %. In view of conformability required in a bearing alloy, content of 3 mass % or less is preferable. Preferable content ranges between 0.02 to 2 mass %.
  • the selective elements (B, Ti, Zr) given in (3) do not contribute to the production of Al—Si—Fe type intermetallic compounds but are incorporated by solid solution into the Al-matrix to improve the fatigue strength of the bearing alloy. This effect cannot be expected in content less than 0.01 mass %. In view of brittleness required in a bearing alloy, content of 2 mass % or less is preferable. Preferable content ranges between 0.02 to 0.5 mass %.
  • FIG. 1 An image of the anaylsis based on idealized distribution of Si particles.
  • FIG. 2 An image of the analysis based on idealized distribution of Si particles viewed in the cross section taken along the thickness direction.
  • FIG. 3 A side view schematically illustrating the roll step.
  • FIG. 4 A chart indicating the wear test conditions.
  • FIG. 5 A chart indicating the fatigue test conditions.
  • FIG. 6 A chart indicating the test results of EXAMPLES and COMPARATIVE EXAMPLES.
  • a billet of Al-based bearing alloy containing Si was cast with a continuous caster. More specifically, using the composition shown in the chart of FIG. 6 as a dissolving material for producing the Al-based bearing alloy, a sheet of Al-based alloy billet was obtained, which was approximately 15 mm thick.
  • the billet was cold rolled multiple times to a predetermined thickness (e.g. 1 mm) to obtain a thin sheet of Al-based bearing alloy.
  • the rolling step is carried out by passing the sheet of billet 111 between a pair of upper and lower rollers 112 and 113 while applying pressure with the rotating rollers 112 and 113 as shown in FIG. 3 .
  • the present embodiment rolls billet 111 at least twice at a high rolling reduction.
  • the rolling reduction of the first roll is set approximately to 70% and the rolling reduction of the second roll is set approximately to 50% slightly lower than the first roll.
  • the obtained Al-based bearing alloy was roll bonded with a steel sheet constituting the metal backing to obtain the bearing forming sheet.
  • the bonding surface of the steel sheet may be controlled to surface roughness of maximum height ranging from 5 to 40 ⁇ m for securing bonding force. Annealing is carried out after the roll bonding for bonding enhancement and eliminating strain.
  • the obtained bearing forming sheet is machined into a semi-cylindrical form to obtain a semi-cylindrical bearing serving as EXAMPLES.
  • the method of manufacturing COMPARATIVE EXAMPLES differs from the method of manufacturing the EXAMPLES in the following respects.
  • the billet is repeatedly rolled in the rolling step to the predetermined thickness (1 mm), and at this instance, the maximum rolling reduction is set to 25% or less as was done conventionally.
  • the obtained Al-based bearing alloy was roll bonded with a steel sheet constituting the metal backing to obtain the bearing forming sheet as was done for the EXAMPLES to manufacture the bearing forming sheet.
  • Annealing is carried out after the roll bonding for bonding enhancement and eliminating strain.
  • the obtained bearing forming sheet is machined into a semi-cylindrical form to obtain a semi-cylindrical bearing serving as COMPARATIVE EXAMPLES.
  • EXAMPLES and COMPARATIVE EXAMPLE were further screened through wear and fatigue tests.
  • the conditions employed in the wear test are indicated in FIG. 4 and the conditions employed in the fatigue test are indicated in FIG. 5 .
  • static load was applied on the inner surface of the bearing in which state the start and stop cycle was repeated for a predetermined time period whereafter wear amount ( ⁇ m) was measured.
  • wear resistance was evaluated based on the results of the foregoing.
  • dynamic load was applied on the inner surface of the bearing and the maximum specific load (MPa) tolerable without fatiguing within the predetermined test time was evaluated as the fatigue resistance.
  • the results are indicated in FIG. 6 .
  • EXAMPLE 8 is compared with COMPARATIVE EXAMPLE 1 to consider the impact of A/a on wear resistance and fatigue resistance.
  • EXAMPLE 8 further showed maximum specific load without fatiguing of 80 MPa and wear amount of 18 ⁇ m.
  • COMPARATIVE EXAMPLE 1 further showed maximum specific load without fatiguing of 60 MPa and wear amount of 25 ⁇ m.
  • EXAMPLES 7 and 8 are compared to consider the impact of the aspect ratio of Si particles on fatigue resistance.
  • the aspect ratio of Si particle was 2.3.
  • EXAMPLE 7 further showed maximum specific load without fatiguing of 90 MPa.
  • the aspect ratio of Si particle was 2.6 and maximum specific load without fatiguing was 80 MPa. It can be understood from the comparison of EXAMPLE 7 and EXAMPLE 8 that the aspect ratio of the Si particles being equal to or less than 2.5 is superior in terms of fatigue resistance as compared to the aspect ratio being greater than 2.5. It has been verified that setting the aspect ratio of the Si particles to range from 1 to 2.5 improves the fatigue resistance.
  • EXAMPLES 5 and 6 are compared to consider the impact of the Si particles adjacent to one another in the thickness direction on wear resistance.
  • the wear amount indicating the wear resistance measured 12 ⁇ m.
  • the wear amount indicating the wear resistance measured 15 ⁇ m.

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  • Chemical & Material Sciences (AREA)
  • Engineering & Computer Science (AREA)
  • Mechanical Engineering (AREA)
  • Materials Engineering (AREA)
  • Metallurgy (AREA)
  • Organic Chemistry (AREA)
  • General Engineering & Computer Science (AREA)
  • Sliding-Contact Bearings (AREA)
US13/583,823 2010-03-10 2011-03-03 Al-based bearing alloy Abandoned US20130004364A1 (en)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
JP2010053033 2010-03-10
JP2010053033 2010-03-10
PCT/JP2011/054913 WO2011111603A1 (ja) 2010-03-10 2011-03-03 Ａｌ基軸受合金

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US (1) US20130004364A1 (ko)
JP (1) JPWO2011111603A1 (ko)
KR (1) KR20120137492A (ko)
DE (1) DE112011100844T5 (ko)
GB (1) GB2491540A (ko)
WO (1) WO2011111603A1 (ko)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN105088024A (zh) * 2015-08-27 2015-11-25 华晨汽车集团控股有限公司 汽车焊接夹具合金材料及其制备方法
CN105088034A (zh) * 2015-08-05 2015-11-25 苏州好洁清洁器具有限公司 一种高强度铝合金管材
US20170282306A1 (en) * 2014-12-23 2017-10-05 Hydro Aluminium Rolled Products Gmbh Aluminium Solder Alloy Free from Si Primary Particles and Method for Producing It

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JP5815630B2 (ja) * 2013-10-02 2015-11-17 大豊工業株式会社 アルミニウム合金および摺動部材

Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4471030A (en) * 1981-10-15 1984-09-11 Taiho Kogyo Co., Ltd. Al-Si Bearing alloy and bearing composite

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5846539B2 (ja) * 1979-12-27 1983-10-17 昭和軽金属株式会社 軸受用アルミニウム合金およびその製造法
JPS5864332A (ja) * 1981-10-15 1983-04-16 Taiho Kogyo Co Ltd アルミニウム系合金軸受
JPS5864333A (ja) * 1981-10-15 1983-04-16 Taiho Kogyo Co Ltd アルミニウム系合金軸受
JPS5864336A (ja) * 1981-10-15 1983-04-16 Taiho Kogyo Co Ltd アルミニウム系合金軸受
JPS5864335A (ja) * 1981-10-15 1983-04-16 Taiho Kogyo Co Ltd アルミニウム系合金軸受
JP3472284B2 (ja) * 2001-10-10 2003-12-02 大同メタル工業株式会社 アルミニウム系軸受合金
JP4564082B2 (ja) * 2008-06-20 2010-10-20 大同メタル工業株式会社 摺動部材

Patent Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4471030A (en) * 1981-10-15 1984-09-11 Taiho Kogyo Co., Ltd. Al-Si Bearing alloy and bearing composite

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20170282306A1 (en) * 2014-12-23 2017-10-05 Hydro Aluminium Rolled Products Gmbh Aluminium Solder Alloy Free from Si Primary Particles and Method for Producing It
CN105088034A (zh) * 2015-08-05 2015-11-25 苏州好洁清洁器具有限公司 一种高强度铝合金管材
CN105088024A (zh) * 2015-08-27 2015-11-25 华晨汽车集团控股有限公司 汽车焊接夹具合金材料及其制备方法

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GB201218114D0 (en) 2012-11-21
KR20120137492A (ko) 2012-12-21
JPWO2011111603A1 (ja) 2013-06-27
WO2011111603A1 (ja) 2011-09-15
GB2491540A (en) 2012-12-05
DE112011100844T5 (de) 2013-01-17

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